In the macaque, neurons in ventral premotor cortex and in the putamen have tactile receptive fields on the face or arms, and corresponding visual receptive fields which extend outward from the tactile fields into the space near the body. For cells with tactile receptive fields on the arm, when the arm is moved, the corresponding visual receptive fields move with it. However, when the eyes move, the visual receptive fields remain stationary, “attached” to the arm. We suggest that these “arm-centered" visual responses play a role in visuo-motor guidance. We predict that other portions of the somatotopic map in premotor cortex and the putamen contain similar receptive fields, centered on the corresponding body parts. This "body-part-centered" representation of space is only one of several ways in which space is represented in the brain.